Development of direct-inverse 3-D methods for applied transonic aerodynamic wing design and analysis

An inverse wing design method was developed around an existing transonic wing analysis code. The original analysis code, TAWFIVE, has as its core the numerical potential flow solver, FLO30, developed by Jameson and Caughey. Features of the analysis code include a finite-volume formulation; wing and fuselage fitted, curvilinear grid mesh; and a viscous boundary layer correction that also accounts for viscous wake thickness and curvature. The development of the inverse methods as an extension of previous methods existing for design in Cartesian coordinates is presented. Results are shown for inviscid wing design cases in super-critical flow regimes. The test cases selected also demonstrate the versatility of the design method in designing an entire wing or discontinuous sections of a wing

Numerical simulation of two and three-dimensional viscous free surface flows in partially-filled containers using a surface capturing approach

A new surface capturing method is developed for numerically simulating viscous free surface flows in partially-filled containers. The method is based on the idea that the flow of two immiscible fluids (specifically, a liquid and a gas) within a closed container is governed by the equations of motion for a laminar, incompressible, viscous, nonhomogeneous (variable density) fluid. By computing the flowfields in both the liquid and gas regions in a consistent manner, the free surface can be captured as a discontinuity in the density field, thereby eliminating the need for special free surface tracking procedures;The numerical algorithm is developed using a conservative, implicit, finite volume discretization of the equations of motion. The algorithm incorporates the artificial compressibility method in conjunction with a dual time stepping strategy to maintain a divergence-free velocity field. A slope-limited, high order MUSCL scheme is adopted for approximating the inviscid flux terms, while the viscous fluxes are centrally differenced. Two different methods are considered for solving the resulting block-banded system of equations;The capabilities of the surface capturing method are demonstrated by calculating solutions to several challenging two and three-dimensional problems. The first test case, the two-dimensional broken dam problem, is considered in detail. Results are presented for several grid sizes, upwind schemes, and limiters, and are compared to experimental data from the literature. The solutions employing high order upwind interpolants and a compressive minmod limiter on the density are found to yield the best results. The two-dimensional, viscous Rayleigh-Taylor instability is examined next. Solutions for a density ratio of two are computed for various Reynolds numbers. Computed perturbation growth rates are shown to be in good agreement with theoretical predictions. Results for the three-dimensional broken dam problem are then presented. The computed free surface motions are found to be quite similar to the two-dimensional case. Finally, two cases involving axisymmetric spin-up in a spherical container are studied. The computed free surface shapes are found to exhibit the characteristic parabolic profiles as steady state conditions are approached

Simulation of thin elastic solids in the incompressible viscous flow using implicit interface representation

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 93-94).This thesis provides a numerical algorithm to solve fluid-structure interaction problems in the Cartesian grid. Unlike the typical Immersed Interfaced Method (IIM), we define thin non-stretchable solid interface with the Level Set function. In addition, we developed a partial differential equation which represents the bending rigidity of the interface. The interface is assumed very thin and has zero elastic stress when it is flat. The interface gives singular forces to the incompressible viscous fluid and the fluid solver handles discontinuities across the interface. Instead of solving two dynamic systems (i.e., fluid and solid), we solve the fluid field only and solve a convection equation of interface with the local fluid velocity. This idea is valid because of viscous fluid (i.e., velocity is continuous across the interface) as we can see frequently in the IIM. The result shows that elastic interface vibrates and converges to an equilibrium state. The oscillatory motion of the interface depends on the viscosity of fluid, Young's modulus and thickness of interface. The results looks correct physically, and they match with the existing IIM results.by Jae Hyung Kim.S.M

The development of a predictive procedure for localised three dimensional river flows

This thesis contains the formulation, development and initial tests of a computer model for the prediction of fully three dimensional turbulent free surface flows typically found at localised areas of river systems. It is the intention that the model will be used to predict flow situations which are fully three dimensional. The model is, therefore, tested against a fully three dimensional test case of flow in a two-stage meandering channel. However, the model is not intended simply to be for computing flows in meandering river channels. Rather the model is intended to be used in a variety of problems which are outlined in the thesis. The Reynolds Averaged Navier-Stokes equations form the basis of the physical system. The Reynolds stresses are represented by two different stress-strain relationships: (1) a linear relationship and (2) a non-linear relationship. These relationships rely on an eddy viscosity and a turbulence time-scale which are calculated from two characterising turbulence quantities, a velocity squared scale, k, and an inverse length scale, . These quantities are computed from differential transport equations. Non-linear stress-strain relationships are relatively new and, it has been argued by their originators, require application to several different problems to fully ascertain their potential for future use. The author addresses this demand by applying them to two new problems. These are flow in a plenum chamber and open channel flow over a backward facing step. The equations are solved by an operator splitting method which, it is argued, allows for an accurate and realistic treatment of the troublesome advection terms at low spatial resolutions. This is thought to be essential since for three dimensional problems owing to computer time limitations achieving grid independent solutions with low order schemes is at present very difficult. The advantage of the present approach is demonstrated with reference to a simple one dimensional analogue

Finite difference method in prolate spheroidal coordinates for freely suspended spheroidal particles in linear flows of viscous and viscoelastic fluids

A finite difference scheme is used to develop a numerical method to solve the flow of an unbounded viscoelastic fluid with zero to moderate inertia around a prolate spheroidal particle. The equations are written in prolate spheroidal coordinates, and the shape of the particle is exactly resolved as one of the coordinate surfaces representing the inner boundary of the computational domain. As the prolate spheroidal grid is naturally clustered near the particle surface, good resolution is obtained in the regions where the gradients of relevant flow variables are most significant. This coordinate system also allows large domain sizes with a reasonable number of mesh points to simulate unbounded fluid around a particle. Changing the aspect ratio of the inner computational boundary enables simulations of different particle shapes ranging from a sphere to a slender fiber. Numerical studies of the latter particle shape allow testing of slender body theories. The mass and momentum equations are solved with a Schur complement approach allowing us to solve the zero inertia case necessary to isolate the viscoelastic effects. The singularities associated with the coordinate system are overcome using L'Hopital's rule. A straightforward imposition of conditions representing a time-varying combination of linear flows on the outer boundary allows us to study various flows with the same computational domain geometry. {For the special but important case of zero fluid and particle inertia we obtain a novel formulation that satisfies the force- and torque-free constraint in an iteration-free manner.} The numerical method is demonstrated for various flows of Newtonian and viscoelastic fluids around spheres and spheroids (including those with large aspect ratio). Good agreement is demonstrated with existing theoretical and numerical results.Comment: 32 pages, 12 figures. Accepted at Journal of Computational Physic

Coupling different discretizations for fluid structure interaction in a monolithic approach

In this thesis we present a monolithic coupling approach for the simulation of phenomena involving interacting fluid and structure using different discretizations for the subproblems. For many applications in fluid dynamics, the Finite Volume method is the first choice in simulation science. Likewise, for the simulation of structural mechanics the Finite Element method is one of the most, if not the most, popular discretization method. However, despite the advantages of these discretizations in their respective application domains, monolithic coupling schemes have so far been restricted to a single discretization for both subproblems. We present a fluid structure coupling scheme based on a mixed Finite Volume/Finite Element method that combines the benefits of these discretizations. An important challenge in coupling fluid and structure is the transfer of forces and velocities at the fluidstructure interface in a stable and efficient way. In our approach this is achieved by means of a fully implicit formulation, i.e., the transfer of forces and displacements is carried out in a common set of equations for fluid and structure. We assemble the two different discretizations for the fluid and structure subproblems as well as the coupling conditions for forces and displacements into a single large algebraic system. Since we simulate real world problems, as a consequence of the complexity of the considered geometries, we end up with algebraic systems with a large number of degrees of freedom. This necessitates the use of parallel solution techniques. Our work covers the design and implementation of the proposed heterogeneous monolithic coupling approach as well as the efficient solution of the arising large nonlinear systems on distributed memory supercomputers. We apply Newton’s method to linearize the fully implicit coupled nonlinear fluid structure interaction problem. The resulting linear system is solved with a Krylov subspace correction method. For the preconditioning of the iterative solver we propose the use of multilevel methods. Specifically, we study a multigrid as well as a two-level restricted additive Schwarz method. We illustrate the performance of our method on a benchmark example and compare the afore mentioned different preconditioning strategies for the parallel solution of the monolithic coupled system

Simulations of thermophoretic deposition in wavy channels

The use of exhaust gas recirculation coolers is important for minimization of harmful NOx emissions from large diesel engines. But the use of the soot filled exhaust leads to the deposition of particles on the fins of the EGR cooler. So it is important to understand the soot deposition mechanisms and geometry effects in order to design an efficient fin geometry that minimizes soot deposition. This study developed a fully implicit code with variable property consideration and boundary fitter coordinates to model the fluid flow, heat transfer, and soot deposition in wavy channels. The code was then used to study laminar and turbulent flow with Reynolds numbers ranging from 300 to 10,000. The inlet fluid temperature was held at 750 K and the wall temperature was varied from 300 K to 750 K. The first set of results is for laminar flow in a wavy channel. Three Reynolds numbers and four wall temperatures were studied for a single wavy geometry. The pressure drop, heat transfer, and soot deposition were predicted for all cases and trends are described. Then the effect of geometry on the pressure drop, heat transfer, and soot deposition in a laminar flow is studied. This is done by comparing the wavy channel results with planar channel results for one Reynolds number and three different wall temperatures. The second set of results is for turbulent flow in a wavy channel. Once again three Reynolds numbers and four wall temperatures were studied. Trends for the pressure drop, heat transfer, and soot deposition are described. Then once again the wavy channel results are compared with planar channel results to illustrate the effect of geometry

Institute for Computational Mechanics in Propulsion (ICOMP)

The Institute for Computational Mechanics in Propulsion (ICOMP) is operated by the Ohio Aerospace Institute (OAI) and the NASA Lewis Research Center in Cleveland, Ohio. The purpose of ICOMP is to develop techniques to improve problem-solving capabilities in all aspects of computational mechanics related to propulsion. This report describes the accomplishments and activities at ICOMP during 1993

Simulation of unsteady free surface flows - code verification and discretisation error

In this work a numerical method for the solution of unsteady, inviscid free surface flows is developed. The method is verified and the behaviour of the error related to the numerical method, as the discretisation is refined, is studied in detail. The work divides into two distinct parts. The first one focuses on the development of the solution method. The method is based on unstructured, two dimensional finite volume method. The free surface boundary conditions are satisfied on the instantaneous free surface and the computational grid tracks the deformation of the surface. Typically, in comparable methods the flow and free surface solutions are solved by time integrating the governing equations in two separate stages, which are iterated. The decoupling of the solutions limits the allowable time step in the integration, which makes the approach computationally expensive. In this work two different approaches are presented for the coupling of the solutions, which relax the time step restriction. The approaches that are proposed differ significantly from the coupling approaches presented previously in the literature in that the implementation into the existing pressure correction type solvers is straightforward. The second part concentrates on the verification of the implementation of the numerical method, i.e. on code verification, and on the investigation of the error related to the discretisation of the continuous problem. In both cases, the analysis is based on the method of manufactured solutions (MMS), in which the governing equations are modified, so that the modified equations have a desired analytical solution. The difference to previous studies is that here the technique has been applied for the verification of an unsteady free surface solution method. The verification of such methods has typically been based on i.a. the use of approximate, high order solutions. MMS has the advantage that the numerical solution can be compared with an exact, analytical solution. It is demonstrated in the work that the governing equations were implemented correctly into the developed method and that the method is of second order of accuracy. In addition to the code verification, MMS is used to study the influence of different discretisations and grid refinement strategies on the local error and its convergence. In case of the verification of the free surface solution method the investigation based on a global error norm is extended with an analysis of the Fourier components of the error. A two parameter, approximate model is presented for the temporal variation of the primary component of the solution, with which it is possible to deepen the verification. The model is also used for an uncertainty estimation

Object-oriented hyperbolic solver on 2D-unstructured meshes applied to the shallow water equations

Fluid dynamics, like other physical sciences, is divided into theoretical and experimental branches. However, computational fluid dynamics (CFD) is third branch of Fluid dynamics, which has aspects of both the previous two branches. CFD is a supplement rather than a replacement to the experiment or theory. It turns a computer into a virtual laboratory, providing insight, foresight, return on investment and cost savings1. This work is a step toward an approach that realise a new and effective way of developing these CFD models